TY - JOUR
T1 - Universal tests for memory words
AU - Morvai, Gusztav
AU - Weiss, Benjamin
PY - 2013
Y1 - 2013
N2 - The main result is a universal pointwise test that, when presented with a set of words $S$ on a finite or countable alphabet ${\cal X}$ that purports to be a set of memory words for a stationary process, will eventually almost surely return the value YES precisely when all positive probability words in $S$ are memory words. For example, if $S$ consists of all of the single letters in ${\cal X}$, then the test will eventually say yes if and only if the process is a Markov chain. Various further positive and negative results of this type are also given.
AB - The main result is a universal pointwise test that, when presented with a set of words $S$ on a finite or countable alphabet ${\cal X}$ that purports to be a set of memory words for a stationary process, will eventually almost surely return the value YES precisely when all positive probability words in $S$ are memory words. For example, if $S$ consists of all of the single letters in ${\cal X}$, then the test will eventually say yes if and only if the process is a Markov chain. Various further positive and negative results of this type are also given.
KW - Statistical learning
KW - stationary processes
KW - stochastic processes
UR - http://www.scopus.com/inward/record.url?scp=84884379900&partnerID=8YFLogxK
U2 - 10.1109/TIT.2013.2268913
DO - 10.1109/TIT.2013.2268913
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AN - SCOPUS:84884379900
SN - 0018-9448
VL - 59
SP - 6873
EP - 6879
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 10
M1 - 6532389
ER -